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The investigation of the ideal class group $Cl_K$ of an algebraic number field $K$ is one of the key subjects of inquiry in algebraic number theory since it encodes a lot of arithmetic information about K. There is a considerable amount of…
Combinatorial problems arising in puzzles, origami, and (meta)material design have rare sets of solutions, which define complex and sharply delineated boundaries in configuration space. These boundaries are difficult to capture with…
In this paper we present efficient algorithmic solutions for several constrained resource allocation, management and discovery problems. We consider new types of resource allocation models and constraints, and we present new geometric…
Techniques for simulating molecules whose conformations satisfy constraints are presented. A method for selecting appropriate moves in Monte Carlo simulations is given. The resulting moves not only obey the constraints but also maintain…
Information bottleneck (IB) and privacy funnel (PF) are two closely related optimization problems which have found applications in machine learning, design of privacy algorithms, capacity problems (e.g., Mrs. Gerber's Lemma), strong data…
This article details the algorithmics in FLSSS, an R package for solving various subset sum problems. The fundamental algorithm engages the problem via combinatorial space compression adaptive to constraints, relaxations and variations that…
Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into…
The Sequential Multiple Knapsack Problem is a special case of Multiple knapsack problem in which the items sizes are divisible. A characterization of the optimal solutions of the problem and a description of the convex hull of all the…
We study a simplification of the well-known Shigesada-Kawasaki-Teramoto model, which consists of two nonlinear reaction-diffusion equations with cross-diffusion. A complete set of Q-conditional (nonclassical) symmetries is derived using an…
The problem of discovering frequent itemsets including rare ones has received a great deal of attention. The mining process needs to be flexible enough to extract frequent and rare regularities at once. On the other hand, it has recently…
There exist many Runge-Kutta methods (explicit or implicit), more or less adapted to specific problems. Some of them have interesting properties, such as stability for stiff problems or symplectic capability for problems with energy…
The cluster algorithm in the fully frustrated Ising model on the square lattice is essentially different from the ones used in other systems. Thus its better understanding is particularly important for finding new lines of development.…
The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of…
This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…
We show that estimating the complexity (mean and distribution) of the instances of a fixed size Constraint Satisfaction Problem (CSP) can be very hard. We deal with the main two aspects of the problem: defining a measure of complexity and…
A Sudoku puzzle often has a regular pattern in the arrangement of initial digits and it is typically made solvable with known solving techniques, called strategies. In this paper, we consider the problem of generating such Sudoku instances.…
The material of this work is aimed at mathematics educators, as well as math specialists with a keen interest in progressions. In this paper, we study the subject of arithmetic, geometric, mixed, and harmonic progressions or sequences. Some…
Combining a set of existing constraint solvers into an integrated system of cooperating solvers is a useful and economic principle to solve hybrid constraint problems. In this paper we show that this approach can also be used to integrate…
Our aim is to explain mathematical programs with equilibrium constraints (MPECs), motivate them through applications, present the main equivalent formulations of equilibrium constraints, and summarize the basic existence theory for optimal…
We discuss how a class of difficult kinematic problems can play an important role in an introductory course in stimulating students' reasoning on more complex physical situations. The problems presented here have an elementary analysis once…